Apple mobility trends data visualization

Introduction

I this notebook we ingest and visualize the mobility trends data provided by Apple, [APPL1].

We take the following steps:

1. Download the data

2. Import the data and summarise it

3. Transform the data into long form

4. Partition the data into subsets that correspond to combinations of geographical regions and transportation types

5. Make contingency matrices and corresponding heat-map plots

6. Make nearest neighbors graphs over the contingency matrices and plot communities

7. Plot the corresponding time series

Data description

From Apple’s page https://www.apple.com/covid19/mobility

About This Data The CSV file and charts on this site show a relative volume of directions requests per country/region or city compared to a baseline volume on January 13th, 2020. We define our day as midnight-to-midnight, Pacific time. Cities represent usage in greater metropolitan areas and are stably defined during this period. In many countries/regions and cities, relative volume has increased since January 13th, consistent with normal, seasonal usage of Apple Maps. Day of week effects are important to normalize as you use this data. Data that is sent from users’ devices to the Maps service is associated with random, rotating identifiers so Apple doesn’t have a profile of your movements and searches. Apple Maps has no demographic information about our users, so we can’t make any statements about the representativeness of our usage against the overall population.

Observations

The observations listed in this subsection are also placed under the relevant statistics in the following sections and indicated with “Observation”.

• The directions requests volumes reference date for normalization is 2020-01-13 : all the values in that column are \(100\).

• From the community clusters of the nearest neighbor graphs (derived from the time series of the normalized driving directions requests volume) we see that countries and cities are clustered in expected ways. For example, in the community graph plot corresponding to “{city, driving}” the cities Oslo, Copenhagen, Helsinki, Stockholm, and Zurich are placed in the same cluster. In the graphs corresponding to “{city, transit}” and “{city, walking}” the Japanese cities Tokyo, Osaka, Nagoya, and Fukuoka are clustered together.

• In the time series plots the Sundays are indicated with orange dashed lines. We can see that from Monday to Thursday people are more familiar with their trips than say on Fridays and Saturdays. We can also see that on Sundays people (on average) are more familiar with their trips or simply travel less.

Load packages

library(Matrix)
library(tidyverse)
library(ggplot2)
library(gridExtra)
library(d3heatmap)
library(igraph)
library(zoo)

Data ingestion

Apple mobile data was provided in this WWW page: https://www.apple.com/covid19/mobility , [APPL1]. (The data has to be download from that web page – there is an “agreement to terms”, etc.)

dfAppleMobility <- read.csv( "~/Downloads/applemobilitytrends-2020-05-26.csv", stringsAsFactors = FALSE)
names(dfAppleMobility) <- gsub( "^X", "", names(dfAppleMobility))
names(dfAppleMobility) <- gsub( ".", "-", names(dfAppleMobility), fixed = TRUE)

dfAppleMobility

Observation: The directions requests volumes reference date for normalization is 2020-01-13 : all the values in that column are \(100\).

Data dimensions:

dim(dfAppleMobility)

[1] 3625  141

Data summary:

summary(as.data.frame(unclass(dfAppleMobility[,1:3]), stringsAsFactors = TRUE))

           geo_type                  region     transportation_type
 city          : 786   Washington County:  22   driving:3048       
 country/region: 153   Franklin County  :  20   transit: 222       
 county        :2090   Jefferson County :  19   walking: 355       
 sub-region    : 596   Madison County   :  18                      
                       Jackson County   :  16                      
                       Montgomery County:  15                      
                       (Other)          :3515                      

Number of unique “country/region” values:

dfAppleMobility %>% 
  dplyr::filter( geo_type == "country/region") %>% 
  dplyr::pull("region") %>%
  unique %>% 
  length

[1] 63

Number of unique “city” values:

dfAppleMobility %>% 
  dplyr::filter( geo_type == "city") %>% 
  dplyr::pull("region") %>%
  unique %>% 
  length

[1] 295

All unique geo types:

lsGeoTypes <- unique(dfAppleMobility[["geo_type"]])
lsGeoTypes

[1] "country/region" "city"           "sub-region"     "county"        

All unique transportation types:

lsTransportationTypes <-  unique(dfAppleMobility[["transportation_type"]])
lsTransportationTypes

[1] "driving" "walking" "transit"

Data transformation

It is better to have the data in long form (narrow form). For that I am using the package “tidyr”.

# lsIDColumnNames <- c("geo_type", "region", "transportation_type") # For the initial dataset released by Apple.
lsIDColumnNames <- c("geo_type", "region", "transportation_type", "alternative_name", "sub-region", "country" )
dfAppleMobilityLongForm <- tidyr::pivot_longer( data = dfAppleMobility, cols = setdiff( names(dfAppleMobility), lsIDColumnNames), names_to = "Date", values_to = "Value" )
dim(dfAppleMobilityLongForm)

[1] 489375      8

Remove the rows with “empty” values:

dfAppleMobilityLongForm <- dfAppleMobilityLongForm[ complete.cases(dfAppleMobilityLongForm), ]
dim(dfAppleMobilityLongForm)

[1] 476938      8

Add the “DateObject” column:

dfAppleMobilityLongForm$DateObject <- as.POSIXct( dfAppleMobilityLongForm$Date, format = "%Y-%m-%d", origin = "1970-01-01" )

Add “day name” (“day of the week”) field:

dfAppleMobilityLongForm$DayName <- weekdays(dfAppleMobilityLongForm$DateObject)

Here is sample of the transformed data:

set.seed(3232)
dfAppleMobilityLongForm %>% dplyr::sample_n( 10 )

Here is summary:

summary(as.data.frame(unclass(dfAppleMobilityLongForm), stringsAsFactors = TRUE))

           geo_type                    region       transportation_type               alternative_name       sub.region              country               Date            Value        
 city          :104538   Washington County:  2926   driving:400197                            :382907             :107065   United States:327180   2020-01-13:  3586   Min.   :   2.43  
 country/region: 20349   Franklin County  :  2660   transit: 29526      's-Gravenhage|Den Haag:   399   Texas     : 26999                : 20349   2020-01-14:  3586   1st Qu.:  73.04  
 county        :277970   Jefferson County :  2527   walking: 47215      Anvers|Antwerpen      :   399   California: 14896   Japan        : 16891   2020-01-15:  3586   Median :  99.43  
 sub-region    : 74081   Madison County   :  2394                       AU                    :   399   Georgia   : 14630   Germany      :  8379   2020-01-16:  3586   Mean   :  96.65  
                         Jackson County   :  2128                       Bâle                  :   399   Virginia  : 13566   Thailand     :  8246   2020-01-17:  3586   3rd Qu.: 116.79  
                         Montgomery County:  1995                       België|Belgique       :   399   Ohio      : 13433   France       :  7448   2020-01-18:  3586   Max.   :1081.37  
                         (Other)          :462308                       (Other)               : 92036   (Other)   :286349   (Other)      : 88445   (Other)   :455422                    
   DateObject                       DayName     
 Min.   :2020-01-13 00:00:00   Friday   :68134  
 1st Qu.:2020-02-15 00:00:00   Monday   :68134  
 Median :2020-03-19 00:00:00   Saturday :68134  
 Mean   :2020-03-19 05:28:25   Sunday   :68134  
 3rd Qu.:2020-04-21 00:00:00   Thursday :68134  
 Max.   :2020-05-26 00:00:00   Tuesday  :68134  
                               Wednesday:68134  

Partition the data into geo types × transportation types:

dfAppleMobilityLongForm %>% 
  dplyr::group_by( geo_type, transportation_type) %>% 
  dplyr::count()

aQueries <- split(dfAppleMobilityLongForm,  dfAppleMobilityLongForm[,c("geo_type", "transportation_type")] )

Heat-map plots

We can visualize the data using heat-map plots.

Remark: Using the contingency matrices prepared for the heat-map plots we can do further analysis, like, finding correlations or nearest neighbors. (See below.)

Cross-tabulate dates with regions:

aMatDateRegion <- purrr::map( aQueries, function(dfX) { xtabs( formula = Value ~ Date + region, data = dfX, sparse = TRUE ) } )
aMatDateRegion <- aMatDateRegion[ purrr::map_lgl(aMatDateRegion, function(x) nrow(x) > 0 ) ]

dfPlotQuery <- purrr::map_df( aMatDateRegion, Matrix::summary, .id = "Type" )
head(dfPlotQuery)

 
          Type i j      x
1 city.driving 1 1 100.00
2 city.driving 2 1 100.73
3 city.driving 3 1 102.86
4 city.driving 4 1 102.65
5 city.driving 5 1 109.39
6 city.driving 6 1 109.62

ggplot2::ggplot(dfPlotQuery) +
  ggplot2::geom_tile( ggplot2::aes( x = j, y = i, fill = log10(x)), color = "white") +
  ggplot2::scale_fill_gradient(low = "white", high = "blue") +
  ggplot2::xlab("Region") + ggplot2::ylab("Date") + 
  ggplot2::facet_wrap( ~Type, scales = "free", ncol = 2)

Here we take a “closer look” to one of the plots using a dedicated d3heatmap plot:

d3heatmap::d3heatmap( x = aMatDateRegion[["country/region.driving"]], Rowv = FALSE )

Nearest neighbors graphs

Graphs overview

Here we create nearest neighbor graphs of the contingency matrices computed above and plot cluster the nodes:

th <- 0.94
aNNGraphs <- 
  purrr::map( aMatDateRegion, function(m) { 
    m2 <- cor(as.matrix(m))
    for( i in 1:nrow(m2) ) {
      m2[i,i] <- 0
    }
    m2 <- as( m2, "dgCMatrix") 
    m2@x[ m2@x <= th ] <- 0
    #m2@x[ m2@x > th ] <- 1
    igraph::graph_from_adjacency_matrix(Matrix::drop0(m2), weighted = TRUE, mode = "undirected")
  })

ind <- 3
ceb <- cluster_edge_betweenness(aNNGraphs[[ind]])  
dendPlot(ceb, mode="hclust", main = names(aNNGraphs)[[ind]])

plot(ceb, aNNGraphs[[ind]], vertex.size=1, vertex.label=NA, main = names(aNNGraphs)[[ind]])

Time series analysis

Time series

In this section for each date we sum all cases over the region-transportation pairs, make a time series, and plot them.

Remark: In the plots the Sundays are indicated with orange dashed lines.

Here we make the time series:

aDateStringToDateObject <- unique( dfAppleMobilityLongForm[, c("Date", "DateObject")] )
aDateStringToDateObject <- setNames( aDateStringToDateObject$DateObject, aDateStringToDateObject$Date )
aDateStringToDateObject <- as.POSIXct(aDateStringToDateObject)
aTSDirReqByCountry <-  purrr::map( aMatDateRegion, function(m) rowSums(m) )

matTS <- do.call( cbind, aTSDirReqByCountry)

zooObj <- zoo::zoo( x = matTS, as.POSIXct(rownames(matTS)) )

Here we plot them:

autoplot(zooObj) +
  aes(colour = NULL, linetype = NULL) +
    facet_grid(Series ~ ., scales = "free_y") +
  geom_vline( xintercept = aDateStringToDateObject[weekdays(aDateStringToDateObject) == "Sunday"], color = "orange", linetype = "dashed", size = 0.3 )

Observation: In the time series plots the Sundays are indicated with orange dashed lines. We can see that from Monday to Thursday people are more familiar with their trips than say on Fridays and Saturdays. We can also see that on Sundays people (on average) are more familiar with their trips or simply travel less.

“Forecast”

He we do “forecast” for code-workflow demonstration purposes – the forecasts should not be taken seriously.

Fit a time series model to the time series:

aTSModels <- purrr::map( names(zooObj), function(x) { forecast::auto.arima( zoo( x = zooObj[,x], order.by = index(zooObj) ) ) } )

aTSModels <- purrr::map( names(zooObj), function(x) forecast::forecast( as.matrix(zooObj)[,x] ) )
names(aTSModels) <- names(zooObj)

Plot data and forecast:

lsPlots <- purrr::map( names(aTSModels), function(x) autoplot(aTSModels[[x]]) + ylab("Volume") + ggtitle(x) )
names(lsPlots) <- names(aTSModels)

do.call( gridExtra::grid.arrange, lsPlots )

References

[APPL1] Apple Inc., Mobility Trends Reports, (2020), apple.com.

[AA1] Anton Antonov, “Apple mobility trends data visualization”, (2020), SystemModeling at GitHub.

[AA2] Anton Antonov, “NY Times COVID-19 data visualization”, (2020), SystemModeling at GitHub.